Inflatable moon (an Early Illusion)
Our ancestors named one of the days of the week - Monday - after the
Earth’s natural satellite. Despite its importance the Moon is
the only celestial body not to retain its original mythological name
but rather to have been given a decidedly more practical identity (Moon,
from the Indo-European root *mens, "the star by which
time is measured"). For the Greeks the Moon was Selene,
twin sister of Apollo, goddess of love and hunting.

And
there is yet another curiosity about the Moon: the Moon Illusion.
Stated simply, the full Moon, when just above the horizon, appears twice
as large as when it is overhead. Yet the Moon, a quarter of a million
miles away from the Earth, always subtends the same angular magnitude
(i. e. the angle the Moon subtends at the eye) wherever it is in the
sky, roughly 1/2 degree (0.52°). The Moon Illusion has been studied
for centuries, and first appeared in a cuneiform inscription on a clay
tablet from the Royal Library at Nineveh (Babylon) dating back to the
7th century B.C.! A satisfactory explanation of the phenomenon is still
being debated but most agree that the Moon Illusion exists. As explained
above, the distance between the Earth and the Moon changes very little
– not enough to cause the effects we see. Furthermore, there is
an optical contradiction. When the Moon is located at the horizon, its
apparent size should be theorically smaller and not larger… As
in fact (as shown in fig. 1 above), the Moon at the horizon is a few
thousands miles farther away than when it is overhead.

People
have thought that the thicker atmosphere along the horizon could act
as a magnifying glass enlarging the image of the full Moon when it is
on the horizon. That could not be the case as there is not enough atmosphere
around the Earth to cause a dramatic lens effect. Anyway, according
to the laws of physics, if the atmosphere was really refracting the
image of the Moon, it would appear smaller!

Some
scientists have proposed that the Moon Illusion effect depends on our
perception of the sky as a flat-topped dome the rim of which appears
further away than the top of the dome. The effect of this error in perspective
is for the Moon overhead to appear smaller than the horizon Moon. The
diagram (fig. 2) opposite shows the apparent location of the Moon at
various points as it travels across the sky. This is the diagram commonly
seen in books promoting this hypothesis… But the diagram can be
misleading! The hemispherical flat-topped dome in the picture is not
of proven relevance to the effect and ought to be omitted as it falsely
suggests a mental process of "projecting" the moon onto that
dome.

Others
have proposed that the Moon Illusion had to do with the fact that the
eye-brain system is designed to work on the horizontal plane, not the
vertical plane. On the horizon we process the Moon image in the optimal
orientation giving us its true apparent size. Tipping our head back
to view the high Moon, we see a non-optimal image. The illusion is not
that the horizon Moon is larger, but that the overhead Moon is smaller
in size than it "ought" to be. Others have argued that comparisons
with buildings and other objects on the horizon are responsible for
the differences between the Moon’s apparent size when looking
horizontally and looking vertically (this explanation is contradicted
by the fact that the Moon Illusion also occurs over open water).

Finally,
here is an explanation that is sufficiently satisfactory. The effect
of this illusion is due mainly to the fact that our brain interprets
the sky as being farther away near the horizon, and closer near the
zenith (directly overhead, see fig. 3 opposite). This isn’t surprising;
look at the sky on a cloudy day and the clouds overhead may be a few
kilometers above you, but near the horizon they might be hundreds of
kilometers away. The Moon, when it’s on the horizon, is interpreted
by your brain as being farther away. Since it’s the same apparent
size as when it’s high up, your brain figures it must be physically
bigger (as illustrated in fig. 4 further below). Otherwise, the distance
would make it look smaller. This effect is the well-known Ponzo Illusion
(fig. 5.a). Actually, the Moon Illusion effect is the result of a mix
of Ebbinghaus size illusion (fig. 5.b) plus Ponzo illusion (see resulting
fig. 6).